Can a circle be filled with a triangle fan?
Create and poke face

You can do this with 2 operations.

F, &#9095; AltP


F (creates a face)
&#9095; AltP (poke face, creating a triangle fan)


See: Mesh -> Face menu for both.

Note for Blender 2.80 users: Shortcut for Poke Faces was removed and the menu entry relocated to Face -> Poke Faces.

Extrude and merge edges

E, Escape, &#9095; AltM, A


E (Extrude)
&#9095; AltM (Merge)


A (Menu accelerator for the  A&#818;t Center option)



Note:


Create face &amp; Poke will assign UV's &amp; vertex colors from surrounding faces (the extrude method will simply extend UV's/colors, which may not be what you want).
Poke uses a more advanced method to calculate the face center point(noticeable when edges aren't evenly spaced).